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Question: use the laplace transform method to solve the following differential...

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Use the Laplace transform method to solve the following differential equations:

a) y ′ − 3y = 0, y(0) = 1

b) y ′′ − y = et , y(0) = 0, y′ (0) = 1

c) y ′ + 4y = t, y(0) = 2

d) y ′′ + 2y ′ + 5y = 0, y(0) = 2, y′ (0) = −8

e) y ′′ + y ′ − 2y = et , y(0) = 1, y′ (0) = −3

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